Question

The below wooden double overhanging beam is under a uniformly distributed load W. The wood is weak along the orientation of the grain (or wood cell fibres) that makes an angle of 30° with the horizontal (see figure). The maximum shear stress on a plane parallel to the grain that the wood can sustain is t,max = 5 MPa, and the maximum normal stress of wood is omax = 25 MPa. The Young modulus of this wood is E=15 GPa. (a) Using w 18 kN/m, check if the beam is safe against failure & Determine the deflections at free ends and at the middle of the beam (b) Determine the value of w so that the maximum deflection of the beam will not exceed 2 mm AND the beam is safe against failure (c) If the uniformly distributed load W on the overhanging parts of the beam is removed (or W is applied over the 2-m span only), will the deflections calculated in question (a) increase or decrease. Explain with details (e.g. sketch) but (d) If an additional concentrated force (vertical & downward direction) is applied in the middle of the beam (w is still applied over its entire length of the beam), will the deflections calculated in question (a) increase or decrease. Explain with details (e.g. sketch) but no calculations. Sketch the bending moment and shear diagrams calculations. Sketch the bending moment and shear diagrams no W 200 mm 300 700 mm 700 mm 2000 mm 60 mm

Answer 1

SelA l9omm 2a0omm 70amm TRA (2+072) 30.6 kN bX 3.4 - dv Sheas fore dingonm uig 2.6 EN S Fomot 12.6EN shess for SFD 0.m A Im A2-6kn° 9kN diram Memant 4.53 ks-mr 4.41 N-m 4.41k.m saar ferca = o Ctive moment 4.55FNm At maximum hegy at moxm 4.41km Shear foras 18KN tmoment 00 - Bfop ghear Atas Floxuaf dinfran tseaus Vaj diym botiom A

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